Modern Regression Analysis in R

Modern Regression Analysis in R

This course is part of Statistical Modeling for Data Science Applications Specialization

Instructor: Brian Zaharatos

Sponsored by Louisiana Workforce Commission

7,143 already enrolled

6 modules

Gain insight into a topic and learn the fundamentals.

4.4

(30 reviews)

Intermediate level

Recommended experience

45 hours to complete

3 weeks at 15 hours a week

Flexible schedule

Learn at your own pace

6 modules

Gain insight into a topic and learn the fundamentals.

4.4

(30 reviews)

Intermediate level

Recommended experience

45 hours to complete

3 weeks at 15 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Articulate some recommended practices for ethical behavior and communication in statistics and data science.
Interpret important components of the MLR model, including the “systematic” and “random” components of the model.
Describe and implement testing-based procedures for model selections and select a “best” model based on a given procedure.

Skills you'll gain

Details to know

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Assessments

2 quizzes, 9 assignments

Taught in English

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This course is part of the Statistical Modeling for Data Science Applications Specialization

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There are 6 modules in this course

This course will provide a set of foundational statistical modeling tools for data science. In particular, students will be introduced to methods, theory, and applications of linear statistical models, covering the topics of parameter estimation, residual diagnostics, goodness of fit, and various strategies for variable selection and model comparison. Attention will also be given to the misuse of statistical models and ethical implications of such misuse.

This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Logo adapted from photo by Vincent Ledvina on Unsplash

In this module, we will introduce the basic conceptual framework for statistical modeling in general, and for linear regression models in particular.

What's included

8 videos3 readings1 quiz1 assignment2 programming assignments1 peer review1 discussion prompt1 ungraded lab

8 videosTotal 82 minutes

Frameworks and Goals of Statistical Modeling14 minutesPreview module
The Assumption of Concept Validity7 minutes
The Linear Regression Model11 minutes
Matrix Representation of the Linear Regression Model15 minutes
Assumptions of Linear Regression9 minutes
The Appropriateness of Linear Regression11 minutes
Interpreting the Linear Regression Model I7 minutes
Interpreting the Linear Regression Model II5 minutes

3 readingsTotal 30 minutes

Earn Academic Credit for your Work!10 minutes
Course Support10 minutes
Assessment Expectations10 minutes

1 quizTotal 30 minutes

The Linear Regression Model30 minutes

1 assignmentTotal 30 minutes

Introduction to Statistical Modeling30 minutes

2 programming assignmentsTotal 180 minutes

Module 1 Autograded120 minutes
Optional Introduction to Jupyter and R60 minutes

1 peer reviewTotal 60 minutes

Module 1 Peer Review Submission60 minutes

1 discussion promptTotal 10 minutes

Introduce Yourself10 minutes

1 ungraded labTotal 60 minutes

Module 1: Peer Reviewed Lab60 minutes

In this module, we will learn how to fit linear regression models with least squares. We will also study the properties of least squares, and describe some goodness of fit metrics for linear regression models.

What's included

9 videos2 assignments1 programming assignment1 peer review1 ungraded lab

9 videosTotal 133 minutes

Introduction to Least Squares12 minutesPreview module
Linear Algebra for Least Squares9 minutes
Deriving the Least Squares Solution20 minutes
Regression Modeling in R: a First Pass19 minutes
Justifying Least Squares: the Gauss-Markov Theorem and Maximum Likelihood Estimation13 minutes
Sums of Squares and Estimating the Error Variance19 minutes
The Coefficient of Determination9 minutes
The Problem of Non-identifiabiliity6 minutes
Regression Modeling in R: a Second Pass22 minutes

2 assignmentsTotal 60 minutes

Least Squares30 minutes
Variability and Identifiability in Regression Models30 minutes

1 programming assignmentTotal 120 minutes

Module 2 Autograded Assignment120 minutes

1 peer reviewTotal 60 minutes

Module 2 Peer Review Submission60 minutes

1 ungraded labTotal 120 minutes

Module 2 Peer Reviewed Lab120 minutes

In this module, we will study the uses of linear regression modeling for justifying inferences from samples to populations.

What's included

8 videos1 reading2 assignments1 programming assignment2 peer reviews1 ungraded lab

8 videosTotal 120 minutes

Motivating Statistical Inference in the Linear Regression Context9 minutesPreview module
The Sampling Distribution of the Least Squares Estimator23 minutes
T-Tests for Individual Regression Parameters14 minutes
T-Tests in R20 minutes
Motivating the F-Test: Multiple Statistical Comparisons8 minutes
The F-Test22 minutes
The F-Test in R10 minutes
Confidence Intervals in the Regression ContextConfidence Intervals in the Regression Context11 minutes

1 readingTotal 30 minutes

Ethics in Statistical Practice and Communication: Five Recommendations30 minutes

2 assignmentsTotal 60 minutes

Statistical Inference: Intro and T-Tests30 minutes
Statistical Inference: the F-tests and Confidence Intervals30 minutes

1 programming assignmentTotal 120 minutes

Module 3 Autograded Assignment120 minutes

2 peer reviewsTotal 120 minutes

Ethics in Statistical Practice and Communication: Five Recommendations60 minutes
Module 3 Peer Review Submission60 minutes

1 ungraded labTotal 60 minutes

Module 3 Peer Reviewed Lab60 minutes

In this module, we will identify how models can predict future values, as well as construct interval estimates for those values. We will also explore the relationship between statistical modelling and causal explanations.

What's included

6 videos1 assignment1 programming assignment1 peer review1 ungraded lab

6 videosTotal 81 minutes

Differentiating Prediction and Explanation12 minutesPreview module
Point Estimates for Prediction10 minutes
Interval Estimates for Prediction9 minutes
Making Predictions Using Real Data in R19 minutes
When Prediction Goes Wrong7 minutes
Defining Causality22 minutes

1 assignmentTotal 30 minutes

Prediction30 minutes

1 programming assignmentTotal 120 minutes

Module 4 Autograded Assignment120 minutes

1 peer reviewTotal 60 minutes

Module 4 Peer Review Submission60 minutes

1 ungraded labTotal 60 minutes

Module 4 Peer Review Lab60 minutes

In this module, we will learn how to diagnose issues with the fit of a linear regression model. In particular, we will use formal tests and visualizations to decide whether a linear model is appropriate for the data at hand.

What's included

6 videos1 quiz1 assignment1 programming assignment1 peer review1 ungraded lab

6 videosTotal 71 minutes

Linear Regression Diagnostic Methods8 minutesPreview module
Violations of the Linearity Assumption12 minutes
Violations of the Independence Assumption15 minutes
Violations of the Constant Variance Assumption11 minutes
Violations of the Normality Assumption9 minutes
Diagnostics in R14 minutes

1 quizTotal 30 minutes

Diagnostics I: Linearity and Independence30 minutes

1 assignmentTotal 30 minutes

Diagnostics II: Constant Variance and Normality30 minutes

1 programming assignmentTotal 120 minutes

Module 5 Autograded Assignment120 minutes

1 peer reviewTotal 60 minutes

Module 5 Peer Review Submission60 minutes

1 ungraded labTotal 120 minutes

Module 5 Peer Review Assignment120 minutes

In this module, we will study methods for model selection and model improvement.. In particular, we will learn when and how to apply model selection techniques such as forward selection and backward selection, criterion-based methods, and will learn about the problem of multicollinearity (also called collinearity).

What's included

10 videos2 assignments1 programming assignment1 peer review1 ungraded lab

10 videosTotal 95 minutes

Motivating Model Selection Methods10 minutesPreview module
Testing-Based Procedures and their Shortfalls8 minutes
Criterion-Based Procedures: AIC15 minutes
Criterion-Based Procedures: BIC7 minutes
Criterion-Based Procedures: Adjusted R-Squared7 minutes
The Mean Squared Prediction Error as a Model Selection Method 4 minutes
Model Selection in R14 minutes
The Problem of Collinearity7 minutes
Diagnosing Multicollinearity 12 minutes
The Problem of Multicollinearity: Solutions and R Implementation 8 minutes

2 assignmentsTotal 60 minutes

Model Selection II: Criterion-based Procedures30 minutes
Multicollinearity30 minutes

1 programming assignmentTotal 180 minutes

Module 6 Autograded Assignment180 minutes

1 peer reviewTotal 60 minutes

Module 6 Peer Review Submission60 minutes

1 ungraded labTotal 60 minutes

Module 6 Peer Review Lab60 minutes

Instructor

Instructor ratings

4.8 (12 ratings)

Brian Zaharatos

University of Colorado Boulder

3 Courses12,164 learners

Offered by

University of Colorado Boulder

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Learner reviews

4.4

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Reviewed on Apr 29, 2024

A lot of work with several peer reviews, but it get you into R for Regression Analysis. Well laid out course. need knowledge of Linear algrebra for this course.

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